[R] Generating unordered, with replacement, samples

Duncan Murdoch murdoch.duncan at gmail.com
Wed Sep 17 21:07:22 CEST 2014

On 17/09/2014 2:25 PM, Giovanni Petris wrote:
> Hello,
> I am trying to interface in my teaching some elementary probability with Monte Carlo ideas. In sampling from a finite population, the number of distinct samples of size 'k' from a population of size 'n' , when individuals are selected with replacement and the selection order does not matter, is choose(n + k -1, k). Does anyone have a suggestion about how to simulate (uniformly!) one of these possible samples? In a Monte Carlo framework I would like to do it repeatedly, so efficiency is of some relevance.
> Thank you in advance!

I forget the details of the derivation of that count, but the number 
suggests it is found by selecting k things without replacement from 
n+k-1.  The sample() function in R can easily give you a sample of k 
integers from 1:(n+k-1); "all" you need to do is map those numbers into 
your original sample of k from n.  For that you need to remember the 
derivation of that formula!

Duncan Murdoch

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